Stationarity with Occasionally Binding Constraints
James A. Duffy, Sophocles Mavroeidis, Sam Wycherley
TL;DR
CKSVAR models endogenously regime-switching multivariate time series under occasionally binding constraints, such as the zero lower bound. By linking stationarity and ergodicity to the stability of a deterministic skeleton, the paper provides sufficient conditions that go beyond linear root criteria and leverages regime-switching theory. Since exact analytic checks are intractable, it introduces computable spectral-radius based criteria—JSR, CJSR, and RJSR—whose bounds are obtained via SDP/SOS methods implemented in thresholdr. The numerical examples illustrate how these criteria guide assessment of stability, showing that exploiting transition constraints yields less conservative bounds and improving inference in nonlinear constrained settings.
Abstract
This paper studies a class of multivariate threshold autoregressive models, known as censored and kinked structural vector autoregressions (CKSVAR), which are notably able to accommodate series that are subject to occasionally binding constraints. We develop a set of sufficient conditions for the processes generated by a CKSVAR to be stationary, ergodic, and weakly dependent. Our conditions relate directly to the stability of the deterministic part of the model, and are therefore less conservative than those typically available for general vector threshold autoregressive (VTAR) models. Though our criteria refer to quantities, such as refinements of the joint spectral radius, that cannot feasibly be computed exactly, they can be approximated numerically to a high degree of precision.